Rotated Rectangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Rotated Rectangle - Geometric Propertiesrotated rectangle 2

  • Rectangle is a quadrilateral with two pair of parallel edges.
  • Interior angles are 90°
  • Exterior angles are 90°
  • Angle \(\;A = B = C = D\)
  • 2 diagonals
  • 4 edges
  • 4 vertexs

Area of a Rotated Rectangle formula

\( \large{ A_{area} = ab  }\)

Perimeter of a Rotated Rectangle formula

\( \large{ P= 2 \left( a + b     \right)  }\)

Side of a Rotated Rectangle formula

\( \large{ a = \frac {P} {2} - b   }\)

\( \large{ b = \frac {P} {2} - a  }\)

Distance from Centroid of a Rotated Rectangle formula

\( \large{ C_x =  \frac {  b \; cos  \; \theta   \; + \;  a \; sin  \; \theta           }  { 2 }   }\)

\( \large{ C_y =  \frac {  a \; cos  \; \theta  \;  + \;  b \; sin  \; \theta           }  { 2 }    }\)

Elastic Section Modulus of a Rotated Rectangle formula

\( \large{ S_x =  \frac { a^2b }  { 6  }  }\)

Polar Moment of Inertia of a Rotated Rectangle formula

\(\large{ J_{z} = \frac {ba}{3}  \left( b^2 + a^2  \right)        }\)

Radius of Gyration of a Rotated Rectangle formula

\(\large{ k_{x} =    \sqrt{   \frac  {  a^2 \;cos^2 \;    \left(    b^2 \; sin^2 \; \theta \;   + \; \theta        \right)    }    {  2  \sqrt 3  }    }      }\)

Second Moment of Area of a Rotated Rectangle formula

\(\large{ I_{x} =    \frac {ba}{12}         \left(     a^2 \; cos^2 \;  \theta  +  b^2  \; sin^2 \;  \theta     \right)            }\)

 

Where:

\(\large{ A }\) = area

\(\large{ a, b }\) = side

\(\large{ C }\) = distance from centroid

\(\large{ I }\) = moment of inertia

\(\large{ J }\) = torsional constant

\(\large{ k }\) = radius of gyration

\(\large{ P }\) = perimeter

\(\large{ S }\) = elastic section modulus

 

Tags: Equations for Structural Steel